Download Expected Coalescence Rate of NS/NS Binaries for Laser Beam

Expected Coalescence Rate
of NS/NS Binaries
for Ground Based Interferometers
Tania Regimbau
OCA/ARTEMIS
on the behalf of
J.A. de Freitas Pacheco, T. Regimbau, S. Vincent, A. Spallicci
The Model

a very small fraction of massive binaries remains
bounded after 2 supernova explosions

the resulting system consist of:
1. a partially reaccelerated pulsar
2. a young pulsar with
- same period evolution (magnetic dipole spin
down) as normal radio pulsars
- same kick velocity as millisecond pulsars (for
which the supernova didn’t disrupt the system
either)
The Galactic Coalescence Rate
 c (t )   f b  NS 
t  *  0
0
R* (t   *   ) P( )d
R* (t ) : star formation rate (Rocha-Pinto et al., 2000)
40
: fraction of formed stars in the range 9-40 M ( =  Am-1.35dm)
9
f b : fraction of massive binaries formed among all stars
 NS : fraction of massive binaries that remain bounded after the second supernova
P( ): probability for a newly formed NS/NS to coalesce in a timescale 
 0 : minimum coalescence time
 * : mean timescale required for the newly formed massive system to evolve into two NSs
The Galactic Star Formation Rate
previous studies:
the star formation rate is proportional to the available mass of
gas as, R*(t) ~ e-at
present work:
the star formation history is reconstructed from observations:
 ages of 552 stars derived from chromospheric activity
index (Rocha-Tinto et al., 2000)
 enhanced periods of star formation at 1 Gyr, 2-5 Gyr and 79 Gyr probably associated with accretion and merger
episodes from which the disk grows and acquires angular
momentum (Peirani, Mohayaee, de Freitas Pacheco, 2004)
The Galactic Coalescence Rate
 c (t )   f b  NS 
t  *  0
0
R* (t   *   ) P( )d
R* (t ) : star formation rate (Rocha-Pinto et al., 2000)
40
: fraction of formed stars in the range 9-40 M ( =  Am-1.35dm)
9
f b : fraction of massive binaries formed among all stars
 NS : fraction of massive binaries that remain bounded after the second supernova
P( ): probability for a newly formed NS/NS to coalesce in a timescale 
 0 : minimum coalescence time
 * : mean timescale required for the newly formed massive system to evolve into two NSs
Numerical Simulations (P(), 0, NS)
 initial parameters:
birth parameters
(M1, M2, a, e)0
 masses: M1, Salpeter IMF, M1/M2: probability derived from observations
 separation: P(a)da=da/a between 2RRoche and 200RRoche
 eccentricity: P(e)de = 2ede
Mass loss
(M1, M2, a, e)1
E>0
 evolution of orbital parameters due to mass loss (stellar wind,
mass transfert, supernova)
 statistical properties
Mass loss
(1.4Mo, M2, a, e)2
  NS= 2.4% (systems that remain bounded after the second supernova)
 P()  0.087/ (probability for a newly formed system to coalesce in a timescale )
disrupted
Supernova 1
E>0
Supernova 2
disrupted
 0 2x105 yr (minimum coalescence time)
NS/NS system
a, e -> 
Vincent, 2002
The Galactic Coalescence Rate
 c (t )   f b  NS 
t  *  0
0
R* (t   *   ) P( )d
R* (t ) : star formation rate (Rocha-Pinto et al., 2000)
40
: fraction of formed stars in the range 9-40 M ( =  Am-1.35dm)
9
f b : fraction of massive binaries formed among all stars
 NS : fraction of massive binaries that remain bounded after the second supernova
P( ): probability for a newly formed NS/NS to coalesce in a timescale 
 0 : minimum coalescence time
 * : mean timescale required for the newly formed massive system to evolve into two NSs
Population Synthesis (fb)
 single radio pulsar properties:
birth parameters
Po, Bo, vk, do…
• Np = 250000 (for 1095 observed)
• birth properties
mean
dispertion
P0 (ms)
240 ± 20
80± 20
ln 0 (s)
11 ± 0.5
3.6 ± 0.2
magnetic
braking
present properties
P, dP/dt, d, S …
 second binary pulsar properties:
• the youngest pulsar has the same:
- period evolution (magnetic dipole spin down) as single radio pulsars
- kick velocity as millisecond pulsars (remains bounded after the supernova)
selection effects:
sky coverage,
cone, flux
+
-
• Nb = 730 (for two observed)

1 1  fb
1   NS

2
N b  NS f b
 NS
Np
 f b  0.136
observed
hidden
Regimbau, 2001&2004
The Local Coalescence Rate
 E LS
 c   S ( fS  fE
)
 S LE
 weighted average over
spiral (fS=65%) and elliptical (fE=35%) galaxies
 same fb and NS as for the Milky Way
 spiral galaxy coalescence rate equal to the Milky Way rate:
S = MW = (1.7±1)x10-5 yr-1
 elliptical galaxy star formation efficiency and IMF estimated
from observations - color & metallicity indices (Idiart,
Michard & de Freitas Pacheco, 2003)
E = 8.6x10-5 yr-1
 c = 3.4x10-5 yr-1
other estimates: ~10-6 – 10-4 yr-1
(Kalogera et al., 2004: 1.8x10-4 yr-1)
Intermitent star
formation history:
modulation in the
coalescence rate
Bulk of stars formed
in the first 1-2 Gyr.
The pairs merging today
were formed with
long coalescence times
(P () ~1/ )
The Detection Rate
 coalescence rate within the volume V=4/3 p D3
 (<D)   c
LV
4
with V= p D3
LMW
3
counts of galaxies from the LEDA catalog:
- 106 galaxies (completness of 84% up to B = 14.5)
- inclusion of the Great Attractor (intersection of
Centaurus Wall and Norma Supercluster) corresponding to
4423 galaxies at Vz = 4844 km/s
 maximum probed distance and mean expected rate
(S/N=7; false alarm rate=1) :
VIRGO
LIGO
LIGO Ad
13 Mpc
1 event/148 yr
14 Mpc
1 event /125 yr
207 Mpc
6 events/yr
Possible Improvements in the Sensitivity…
 gain in the VIRGO thermal mirror noise band (52-148 Hz):
reduction of all noises in the band by a factor 10 (Spallicci, 2003; Spallicci et
al., submitted)
gain throughout VIRGO full bandwidth
reduction of pendulum noise by a factor 28, thermal mirror 7, shot 4 (Punturo,
2004; Spallicci et al., submitted)
• maximum probed distance: 100 Mpc
• detection rate: 1.5 events / yr
 use networks of detectors:
LIGO-H/LIGO-L/VIRGO(Pai, Dhurandhar & Bose, 2004)
• false alarm rate = 1, detection probability = 95%
• maximum probed distance: 22 Mpc
• detection rate: 1 events / 26 yrs
Work in progress

compute the GW stochastic background produced by the superposition of all
the NS/NS binaries
analytical approach
integration up to to z~6

numerical approach
generating extragalactic populations of NS/NS binaries

Extra slides
PSR J0737-3039 A+B
.
.
P
dP/dt
Bsurf
A
B
22.7 ms
1.7 x 10-18
6 x 109 G
2.77 s
0.88 x 10-15
1.6 x 1012 G
Kalogera, Kim, Lorimer et al., 2004
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Numerical simulations
sample of 3 galactic coalescing pulsars, (P, dP/dt)i
populate a model galaxy (P(L, R, z)) with Ntot pulsars with (P, dP/dt)i
model radiotelescope survey selection effects and compute Nobsi
Statistics
Nobsi follows a Poisson distribution of mean <Nobs>i
<Nobs>i = a Ntot
bayesian statistic to compute Pi(Ntot)
i
coalescence rate
Ri = Ntoti/life fb
P(Ri) with mean and confidence level
combine P(Ri) to obtain P(R)